GTO_hyp Class Reference

The GTO_hyp class is a user interface for the graph transform algorithm. This class should be used in the saddle case for a one-dimensional manifold, like an invariant closed curve. More...

Public Members

Static Public Members

Detailed Description

This class has two related functions. One allows the user to iterate the graph transform algorithm to convergence for a fixed value of a specified parameter in the dynamical system. The other function lets the user specify a parameter range over which to continue the invariant manifold. The initial data needed to create an object of this class are a discrete one dimensional manifold, together with discrete normal data and a discrete stable/unstable splitting. The graph transform algorithm iterates this initial data. Before an object of this class may be created, a "map" (representing the dynamical system) must be created, a "manifold_hyp" (representing the initial data) must be created, and two "graphMan_hyp" objects (representing the current and next manifolds of the iteration) must be created.

Member Function Documentation

GTO_hyp::GTO_hyp(int bracketMesh,REAL xacc,REAL pNeigh,map *fPtr,manifold_hyp *NBManPtr, graphMan_hyp *gMan1Ptr,graphMan_hyp *gMan2Ptr,REAL bndryTol, Matrix<int> *bndryEltPtr)

The explicit constructor for the class GTO_hyp. This is the only accessible constructor for this class.

Parameters:: bracketMesh - a positive integer specifying the mesh to use in finding sign changes of various real-valued functions.; xacc - a "REAL" value specifying the accuracy of a one dimensional root-finding method.; pNeigh - a "REAL" value which gives a distance from the initial invariant manifold within which the canonical projection onto the manifold is defined.; fPtr - a pointer to a "map" which gives the dynamical system.; NBManPtr - a pointer to a "manifold_hyp" representing the initial manifold of the graph transform iteration.; gMan1Ptr - a pointer to a "graphMan_hyp" which represents the current manifold in the graph transform iteration, which is a graph over the initial manifold (a "manifold_hyp"). This "graphMan_hyp" should be zeroed before being passed to the constructor.; gMan2Ptr - a pointer to a "graphMan_hyp" which represents the next manifold in the graph transform iteration, which is a graph over the initial manifold (the same "manifold_hyp" as above). This "graphMan_hyp" should be zeroed before being passed to the constructor.; bndryTol - a "REAL" value used only in the case of truncated coordinates, to determine if an element is near the boundary.; bndryEltPtr - a pointer to a "Matrix" of ints, used only in the case of truncated coordinates, which keeps track of whether an element is a boundary element.

Returns:: a GTO_hyp object.

int GTO_hyp::continuation(int contMesh,REAL start,REAL end,REAL gtAcc,REAL splitgtAcc,char fname[5])

This member provides the ability to continue the invariant manifold over a parameter range.

Parameters:: contMesh - an integer specifying the continuation step size as a fraction of the continuation interval.; start - a "REAL" number giving the initial value of the continuation parameter.; end - a "REAL" number giving the value of the continuation parameter to attempt continuation to.; gtAcc - a "REAL" value specifying the convergence criterion for the graph transform algorithm.; splitgtAcc - a "REAL" value specifying the convergence criterion for the linear graph transform algorithm which updates the hyperbolic splitting.; fname - a character array with length 5 which specifies the names of the files which the member outputs data to. (there are two output files, a .dat file and a .vect file)

Returns:: an integer specifying the number of continuation steps completed.

Examples:: d1SaddleODE.C.

int GTO_hyp::iterate(int fullOutput,int gtMaxit,REAL gtAcc,char fname[5])

This member provides the ability to iterate the graph transform algorithm to convergence.

Parameters:: fullOutput - an integer with value -1, 0, or 1 specifying the degree of output. (-1 = no graphical output. 0 = graphical output of final manifold computed upon convergence. 1 = graphical output of each step.); gtMaxit - a positive integer specifying the maximum number of iterations to perform before giving up.; gtAcc - a "REAL" value specifying the convergence criterion for the graph transform algorithm.; fname - a character array with length 5 specifying the file names for the output files (.dat and .vect files).

Returns:: an integer giving the number of graph transform iterates completed, -1 if gtMaxit is exceeded.